Short time existence for higher order curvature flows with and without boundary conditions

Wu, Yuhan

doi:10.1007/978-3-030-62497-2_61

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2024

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Cited by 2 publications

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“…Of higher order curvature flows of closed planar curves, the fourth order cases of the curve diffusion flow and the elastic flow are the most well-studied. Important early work includes [K,LS,LS2,L,L2,P,W,W2]. There is also the work of Giga and Ito [GI,GI2] showing that curves may lose embeddedness or convexity under the curve diffusion flow.…”

Section: Introductionmentioning

confidence: 99%

The length-constrained ideal curve flow

McCoy¹,

Wheeler²,

Wu³

2020

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A recent article [AMWW] considered the so-called 'ideal curve flow', a sixth order curvature flow that seeks to deform closed planar curves to curves with least variation of total geodesic curvature in the L 2 sense. Critical in the analysis there was a length bound on the evolving curves. It is natural to suspect therefore that the length-constrained ideal curve flow should permit a more straightforward analysis, at least in the case of small initial 'energy'. In this article we show this is indeed the case, with suitable initial data providing a flow that exists for all time and converges smoothly and exponentially to a multiply-covered round circle of the same length and winding number as the initial curve.

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Section: Introductionmentioning

confidence: 99%